Why is deductive logic also called symbolic logic and mathematical logic.

Because logic uses mathmatical symbols.

Excuse me, but it IS an answer. Logic uses words, then uses symbols to represent those words. Those symbols are frequently taken from mathmatics. Perhaps you should gain a better understanding of the basics of logic so you can understand when an answer is, in fact, presented to you.

Deductive logic certainly uses symbols - but it is never called symbolic logic.
Many other mathematical techniques also use symbols.

Go through this material and tell me if you find the word "symbolic logic":

http://en.wikipedia.org/wiki/Deductive_logic

http://www.answers.com/deductive%20logic